The universal approximation property is an important characteristic of models employed in the solution of machine learning problems. The possibility of approximating within a desired precision any Borel measurable function guarantees the generality of the considered approach.
ANALYZING GENE EXPRESSION DATA FOR PEDIATRIC AND ADULT CANCER DIAGNOSIS USING LOGIC LEARNING MACHINE AND STANDARD SUPERVISED METHODS
In this investigation the performance of LLM in classifying patients with cancer was evaluated using a set of eight publicly available gene expression databases for cancer diagnosis.
LLM accuracy was assessed by summary ROC curve (sROC) analysis and estimated by the area under an sROC curve (sAUC).
Its performance was compared in cross validation with that of standard supervised methods, namely: decision tree, artificial neural network, support vector machine (SVM) and k-nearest neighbor classifier.
LLM showed an excellent accuracy (sAUC = 0.99, 95%CI: 0.98–1.0) and outperformed any other method except SVM.
The straightforward rules generated by LLM could consequently contribute to a better understanding of cancer biology, potentially addressing therapeutic approaches.
APPROXIMATION PROPERTIES OF POSITIVE BOOLEAN FUNCTIONS
TRAINING DIGITAL CIRCUITS WITH HAMMING CLUSTERING
- A new algorithm, called Hamming clustering (HC), for the solution of classification problems with binary inputs is proposed. It builds a logical network containing only AND, OR, and NOT ports which, in addition to satisfying all the input–output pairs included in a given finite consistent training set, is able to reconstruct the underlying Boolean function.
EFFICIENT CONSTRUCTIVE TECHNIQUES FOR TRAINING SWITCHING NEURAL NETWORKS
- In this paper a general constructive approach for training neural networks in classification problems is presented. This approach is used to construct a particular connectionist model, named Switching Neural Network (SNN), based on the conversion of the original problem in a Boolean lattice domain.
SWITCHING NEURAL NETWORKS: A NEW CONNECTIONIST MODEL FOR CLASSIFICATION
A new connectionist model, called Switching Neural Network (SNN), for the solution of classification problems is presented. SNN includes a first layer containing a particular kind of A/D converters, called latticizers, that suitably transform input vectors into binary strings. Then, the subsequent two layers of an SNN realize a positive Boolean function that solve in a lattice domain the original classification problem.
COUPLING LOGICAL ANALYSIS OF DATA AND SHADOW CLUSTERING FOR PARTIALLY DEFINED POSITIVE BOOLEAN FUNCTION RECONSTRUCTION
The problem of reconstructing the AND-OR expression of a partially defined positive Boolean function (pdpBf) is solved by adopting a novel algorithm, denoted by LSC, which combines the advantages of two efficient techniques, Logical Analysis of Data (LAD) and Shadow Clustering (SC). The kernel of the approach followed by LAD consists in a breadth-first enumeration of all the prime implicants whose degree is not greater than a fixed maximum d. In contrast, SC adopts an effective heuristic procedure for retrieving the most promising logical products to be included in the resulting AND-OR expression. Since the computational cost required by LAD prevents its application even for relatively small dimensions of the input domain, LSC employs a depth-first approach, with asymptotically linear memory occupation, to analyze the prime implicants having degree not greater than d. In addition, the theoretical analysis proves that LSC presents almost the same asymptotic time complexity as LAD. Extensive simulations on artificial benchmarks validate the good behavior of the computational cost exhibited by LSC, in agreement with the theoretical analysis. Furthermore, the pdpBf retrieved by LSC always shows a better performance, in terms of complexity and accuracy, with respect to those obtained by LAD.